Remove skin from salmon fillet: With a sharp knife, cut a small corner of the skin away from the flesh. Gently pull and slice off remaining skin, removing as little flesh as possible. Discard skin; coarsely chop salmon.
Heat gas grill to medium-high or coals in charcoal grill to medium-hot. Transfer salmon to a food processor, along with scallions, 1 tablespoon of the dill, the lemon zest, panko, salt and pepper. Pulse until salmon is the consistency of ground beef but still has some shape. Do not overprocess.
Form mixture into 4 patties, each about 3 1/2 inches in diameter. Coat patties with nonstick cooking spray. Grill patties 5 minutes. Flip over and continue to grill another 5 minutes. Meanwhile, stir remaining 1 tablespoon dill into tartar sauce. Divide lettuce evenly among buns. Top each with a burger patty and 1 tablespoon tartar sauce.